Formulate All

Objective

Confidence: 5/5
Minimizel=1LOpeningCostlYl+l=1Lc=1CTransportationCostlcXlcMinimize \sum_{l=1}^{L} \text{OpeningCost}_l \cdot Y_l + \sum_{l=1}^{L} \sum_{c=1}^{C} \text{TransportationCost}_{lc} \cdot X_{lc}

Constraints

Confidence: 5/5
c=1CCustomerDemand[c]X[l,c]MaxCapacity[l]Y[l],l{1,,L}\sum_{c=1}^{C} CustomerDemand[c] \cdot X[l, c] \leq MaxCapacity[l] \cdot Y[l], \quad \forall l \in \{1, \ldots, L\}
Confidence: 5/5
l=1LXl,c=CustomerDemandc,c{1,2,,C}\sum_{l=1}^{L} X_{l,c} = CustomerDemand_{c}, \quad \forall c \in \{1,2,\ldots,C\}
Confidence: 5/5
NumberOfFacilitiesOpened=l=1LYl\text{NumberOfFacilitiesOpened} = \sum_{l=1}^{L} Y_l
Confidence: 5/5
CustomerAssignmentsl,cZ+,l{1,,L},c{1,,C}CustomerAssignments_{l,c} \in \mathbb{Z}^+, \forall l \in \{1, \ldots, L\}, \forall c \in \{1, \ldots, C\}

Variables

SymbolShapeDefinitionDomain